Rinse and halve the Brussels sprouts, trimming off any tough or discolored ends. Cut the chicken breast into evenly sized bite-sized pieces. Mince the garlic and ginger finely.

In a small bowl, whisk together the honey, soy sauce, minced garlic, and minced ginger until fully combined. Set the sauce aside.

Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the Brussels sprouts cut-side down in a single layer. Cook without moving for 5 to 7 minutes until deeply golden and caramelized. Stir and cook for another 2 to 3 minutes until just tender. Remove from the skillet and set aside.

Add the remaining 1 tablespoon of olive oil to the same skillet. Season the chicken pieces with salt and pepper. Add to the hot skillet in a single layer without crowding. Cook, stirring occasionally, for 6 to 8 minutes until browned and cooked through to an internal temperature of 165 degrees F.

Return the Brussels sprouts to the skillet with the chicken. Pour the honey garlic sauce over everything and toss to coat evenly. Simmer over medium-low heat for 2 to 3 minutes, stirring frequently, until the sauce thickens into a glossy glaze. Watch the heat carefully to prevent the honey from burning.

Remove from heat. Sprinkle with sesame seeds and chopped green onions if desired. Serve immediately over steamed rice, quinoa, or noodles.